Multipoles are the pieces we obtain by cutting some edges of a cubic graph in one or more points. As a result of the cut, a multipole M has vertices attached to a dangling edge with one free end, and isolated edges with ...

We prove that the maximum degree Δn of a random series-parallel graph with n vertices
satisfies Δn/ log n → c in probability, and EΔn ∼ c log n for a computable constant c > 0.
The same kind of result holds for 2-connected ...